In this note, I consider the main measures associated with structural holes, namely effective size, redundancy, local constraint and constraint, and derive simple formulas from the adjacency matrix of the network.
This might help to interpret these measures and also produces intuitive and naive algorithms based on matrix multiplications which work fairly well on moderately large networks (see Figure REF ).
However, while this approach is clean and simple, it has clear limitations when the network under analysis is very large.
In such a case, one should avoid storing explicitly the matrices and should preferably rely on distributed algorithms and more advanced techniques for triangle listing with vertex orderings and neighborhood markers [1]}, [2]}.
